Details

Time bar (total: 18.0s)

analyze125.0ms (0.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
0%28.1%71.9%3
3.5%24.6%71.9%4
5.3%22.8%71.9%5
10.5%17.5%71.9%6
14%14%71.9%7
19.1%9%71.9%8
24.6%3.5%71.9%9
25.1%3%71.9%10
25.8%2.3%71.9%11
26.3%1.8%71.9%12
26.6%1.5%71.9%13
26.9%1.2%71.9%14
Compiler

Compiled 39 to 27 computations (30.8% saved)

sample40.0ms (0.2%)

Algorithm
intervals
Results
12.0ms200×body128valid
6.0ms21×body512valid
6.0ms256×pre128true
5.0ms21×body1024valid
2.0ms13×body256valid
0.0msbody2048valid
Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify160.0ms (0.9%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
0537143

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 25.2b

Counts
2 → 1
Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.3b
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
1.7b
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
21.6b
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite105.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity_binary64_1101
54×times-frac_binary64_1107
34×add-sqr-sqrt_binary64_1123
30×add-cube-cbrt_binary64_1136
20×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
14×flip3-+_binary64_1104 associate-/r/_binary64_1047 flip-+_binary64_1075
12×distribute-lft-out_binary64_1052
10×associate-/l*_binary64_1046
associate-/l/_binary64_1048
frac-times_binary64_1111
div-inv_binary64_1098 div-exp_binary64_1152 cbrt-undiv_binary64_1135 associate-/r*_binary64_1045
add-log-exp_binary64_1140 pow1_binary64_1162 flip--_binary64_1076 flip3--_binary64_1105 cancel-sign-sub-inv_binary64_1067
associate-*r*_binary64_1041
distribute-lft-in_binary64_1050 associate-*r/_binary64_1043 associate-*l*_binary64_1042 associate-*l/_binary64_1044 distribute-rgt-in_binary64_1051
cbrt-unprod_binary64_1134 prod-exp_binary64_1150
frac-2neg_binary64_1112 sub-neg_binary64_1094 clear-num_binary64_1100
*-commutative_binary64_1032 difference-of-squares_binary64_1070 sum-log_binary64_1192 distribute-lft-out--_binary64_1053 +-commutative_binary64_1031 pow-prod-down_binary64_1172 unswap-sqr_binary64_1069
Counts
4 → 148
Calls

4 calls:

38.0ms
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
21.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
17.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
10.0ms
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))

series732.0ms (4.1%)

Counts
4 → 12
Calls

4 calls:

346.0ms
(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
291.0ms
(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
66.0ms
(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
29.0ms
(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))

simplify104.0ms (0.6%)

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
060365958

prune303.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New15010160
Fresh000
Picked101
Done000
Total15110161

Merged error: 7.7b

Counts
161 → 10
Compiler

Compiled 6864 to 3512 computations (48.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
0.5b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
1.4b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
3.2b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite158.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
321×times-frac_binary64_1107
290×*-un-lft-identity_binary64_1101
211×add-sqr-sqrt_binary64_1123
140×add-cube-cbrt_binary64_1136
90×associate-*r*_binary64_1041
44×distribute-lft-out_binary64_1052
31×difference-of-squares_binary64_1070 distribute-lft-out--_binary64_1053
26×associate-/l*_binary64_1046
24×associate-/r/_binary64_1047
20×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
15×flip3-+_binary64_1104 flip-+_binary64_1075
12×div-inv_binary64_1098
div-exp_binary64_1152 cbrt-undiv_binary64_1135 associate-/r*_binary64_1045
add-log-exp_binary64_1140 pow1_binary64_1162
associate-*l*_binary64_1042
cbrt-unprod_binary64_1134 prod-exp_binary64_1150 associate-/l/_binary64_1048 unswap-sqr_binary64_1069 div-sub_binary64_1106
frac-times_binary64_1111 frac-2neg_binary64_1112 clear-num_binary64_1100 associate-*l/_binary64_1044
*-commutative_binary64_1032 sum-log_binary64_1192 flip--_binary64_1076 flip3--_binary64_1105 associate-*r/_binary64_1043 +-commutative_binary64_1031 pow-prod-down_binary64_1172
Counts
4 → 295
Calls

4 calls:

45.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
28.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
21.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
11.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series868.0ms (4.8%)

Counts
4 → 12
Calls

4 calls:

349.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
294.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
169.0ms
(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
57.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify152.0ms (0.8%)

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0501413438

prune702.0ms (3.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3016307
Fresh729
Picked101
Done000
Total3098317

Merged error: 7.6b

Counts
317 → 8
Compiler

Compiled 14680 to 7738 computations (47.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
0.5b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
1.4b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
3.2b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite149.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
162×times-frac_binary64_1107
152×*-un-lft-identity_binary64_1101
117×add-sqr-sqrt_binary64_1123
90×associate-*r*_binary64_1041
76×add-cube-cbrt_binary64_1136
22×distribute-lft-out_binary64_1052
16×difference-of-squares_binary64_1070 distribute-lft-out--_binary64_1053
15×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
12×associate-/r/_binary64_1047 cbrt-prod_binary64_1132
10×flip3-+_binary64_1104 flip-+_binary64_1075
add-log-exp_binary64_1140 pow1_binary64_1162 div-inv_binary64_1098
associate-/l*_binary64_1046
div-exp_binary64_1152 cbrt-undiv_binary64_1135 associate-*l*_binary64_1042
cube-prod_binary64_1129 cbrt-unprod_binary64_1134 unpow-prod-down_binary64_1180 prod-exp_binary64_1150 unswap-sqr_binary64_1069 associate-/r*_binary64_1045
frac-times_binary64_1111 associate-/l/_binary64_1048 cube-div_binary64_1130 associate-*l/_binary64_1044 cbrt-div_binary64_1133
*-commutative_binary64_1032 cube-mult_binary64_1131 pow1/3_binary64_1183 frac-2neg_binary64_1112 sum-log_binary64_1192 clear-num_binary64_1100 flip--_binary64_1076 flip3--_binary64_1105 associate-*r/_binary64_1043 unpow3_binary64_1167 +-commutative_binary64_1031 pow-prod-down_binary64_1172 sqr-pow_binary64_1073 div-sub_binary64_1106 rem-cbrt-cube_binary64_1125
Counts
4 → 191
Calls

4 calls:

47.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
30.0ms
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
29.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
12.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.1s (5.9%)

Counts
4 → 12
Calls

4 calls:

354.0ms
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
344.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
304.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
56.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify116.0ms (0.6%)

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
050547900

prune489.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1967203
Fresh257
Picked101
Done000
Total19912211

Merged error: 7.6b

Counts
211 → 12
Compiler

Compiled 10476 to 5831 computations (44.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(pow.f64 (pow.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3) 1/3)
0.5b
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
1.4b
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
3.2b
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite155.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
162×times-frac_binary64_1107
153×*-un-lft-identity_binary64_1101
118×add-sqr-sqrt_binary64_1123
90×associate-*r*_binary64_1041
77×add-cube-cbrt_binary64_1136
22×distribute-lft-out_binary64_1052
17×add-exp-log_binary64_1139
16×difference-of-squares_binary64_1070 distribute-lft-out--_binary64_1053
15×unpow-prod-down_binary64_1180 add-cbrt-cube_binary64_1137
12×associate-/r/_binary64_1047
flip3-+_binary64_1104 flip-+_binary64_1075
add-log-exp_binary64_1140 pow1_binary64_1162 div-inv_binary64_1098
associate-/l*_binary64_1046
pow-exp_binary64_1169 div-exp_binary64_1152 cbrt-undiv_binary64_1135 associate-*l*_binary64_1042
cube-prod_binary64_1129 cbrt-unprod_binary64_1134 prod-exp_binary64_1150 pow-unpow_binary64_1178 unswap-sqr_binary64_1069 associate-/r*_binary64_1045
frac-times_binary64_1111 associate-/l/_binary64_1048 associate-*l/_binary64_1044 sqr-pow_binary64_1073 pow-to-exp_binary64_1170
*-commutative_binary64_1032 cube-mult_binary64_1131 unpow1/3_binary64_1168 pow-pow_binary64_1173 frac-2neg_binary64_1112 sum-log_binary64_1192 clear-num_binary64_1100 flip--_binary64_1076 flip3--_binary64_1105 associate-*r/_binary64_1043 unpow3_binary64_1167 +-commutative_binary64_1031 pow-prod-down_binary64_1172 div-sub_binary64_1106
Counts
4 → 197
Calls

4 calls:

43.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
37.0ms
(pow.f64 (pow.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3) 1/3)
30.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
11.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series6.9s (38.3%)

Counts
4 → 12
Calls

4 calls:

6.2s
(pow.f64 (pow.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3) 1/3)
357.0ms
(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
297.0ms
(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
55.0ms
(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify126.0ms (0.7%)

Algorithm
egg-herbie
Counts
209 → 209
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
052458090

prune506.0ms (2.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New2054209
Fresh11011
Picked101
Done000
Total20714221

Merged error: 7.3b

Counts
221 → 14
Compiler

Compiled 10091 to 5682 computations (43.7% saved)

regimes1.5s (8.5%)

Compiler

Compiled 29012 to 18892 computations (34.9% saved)

bsearch8.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067110
167110

end0.0ms (0%)

sample3.5s (19.2%)

Algorithm
intervals
Results
377.0ms6468×body128valid
185.0ms8000×pre128true
169.0ms717×body1024valid
85.0ms490×body512valid
33.0ms290×body256valid
10.0ms35×body2048valid
Compiler

Compiled 4195 to 2729 computations (34.9% saved)

Profiling

Loading profile data...