Details

Time bar (total: 13.8s)

analyze2.0s (14.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
1.6%98.3%0.1%8
2.3%97.5%0.1%9
7.4%90.9%1.7%10
9.2%87.4%3.5%11
11.7%83.5%4.8%12
15.2%76%8.8%13
16.4%72%11.6%14
Compiler

Compiled 26 to 22 computations (15.4% saved)

sample104.0ms (0.8%)

Algorithm
1×intervals
Results
47.0ms85×body1024valid
17.0ms47×body512valid
13.0ms104×body128valid
6.0ms50×body128invalid
5.0ms20×body256valid
2.0ms5×body512invalid
1.0ms2×body1024invalid
1.0ms3×body256invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify140.0ms (1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0493135
1493135

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
35.6b
Counts
2 → 1
Compiler

Compiled 46 to 38 computations (17.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
3.9b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
14.1b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
18.8b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite73.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
108×add-exp-log_binary64_116
58×prod-exp_binary64_127
52×add-cbrt-cube_binary64_114
28×times-frac_binary64_84
26×add-sqr-sqrt_binary64_100 cbrt-unprod_binary64_111
24×div-exp_binary64_129
20×pow1_binary64_139
19×*-un-lft-identity_binary64_78
18×associate-*l*_binary64_19
17×add-cube-cbrt_binary64_113
16×associate-*l/_binary64_21
12×associate-/l*_binary64_23
10×unpow-prod-down_binary64_157 frac-times_binary64_88 associate-*r*_binary64_18 pow-prod-down_binary64_149 cube-prod_binary64_106
8×tan-quot_binary64_237 pow-exp_binary64_146 pow-to-exp_binary64_147 cbrt-undiv_binary64_112
6×associate-*r/_binary64_20
5×unswap-sqr_binary64_46
4×add-log-exp_binary64_117 flip-+_binary64_52 sqr-pow_binary64_50 flip3-+_binary64_81
3×cube-mult_binary64_108 *-commutative_binary64_9 unpow3_binary64_144
2×div-inv_binary64_75
1×distribute-lft-in_binary64_27 distribute-rgt-in_binary64_28 frac-2neg_binary64_89 associate-/r*_binary64_22 clear-num_binary64_77 distribute-lft-out_binary64_29
Counts
4 → 159
Calls

4 calls:

22.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
12.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
10.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
10.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

series667.0ms (4.8%)

Counts
4 → 12
Calls

4 calls:

390.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
183.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
67.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
26.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify74.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
055553677

prune270.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New16110171
Fresh000
Picked101
Done000
Total16210172
Error
16.7b
Counts
172 → 10
Compiler

Compiled 5033 to 2764 computations (45.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.3b
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.3b
(*.f64 (/.f64 t l) (sin.f64 k))
10.7b
(/.f64 (*.f64 t t) l)
14.1b
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite72.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
120×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
70×cbrt-unprod_binary64_111 prod-exp_binary64_127
44×associate-*l/_binary64_21
34×frac-times_binary64_88
29×pow1_binary64_139
21×add-sqr-sqrt_binary64_100 cbrt-undiv_binary64_112 div-exp_binary64_129
18×*-un-lft-identity_binary64_78
17×pow-prod-down_binary64_149
16×tan-quot_binary64_237 add-cube-cbrt_binary64_113
15×associate-*l*_binary64_19
14×associate-*r/_binary64_20
13×times-frac_binary64_84
10×associate-*r*_binary64_18
8×flip-+_binary64_52 flip3-+_binary64_81
4×add-log-exp_binary64_117
3×*-commutative_binary64_9 associate-/r*_binary64_22
2×div-inv_binary64_75 unswap-sqr_binary64_46
1×distribute-lft-in_binary64_27 distribute-rgt-in_binary64_28 frac-2neg_binary64_89 associate-/l*_binary64_23 clear-num_binary64_77 distribute-lft-out_binary64_29
Counts
4 → 159
Calls

4 calls:

26.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
14.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
5.0ms
(/.f64 (*.f64 t t) l)

series661.0ms (4.8%)

Counts
4 → 12
Calls

4 calls:

396.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
191.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
60.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
13.0ms
(/.f64 (*.f64 t t) l)

simplify92.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049814094
149814094

prune252.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1638171
Fresh369
Picked101
Done000
Total16714181
Error
10.7b
Counts
181 → 14
Compiler

Compiled 5322 to 2673 computations (49.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.5b
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
2.3b
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.3b
(*.f64 (/.f64 t l) (sin.f64 k))
14.1b
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite103.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
151×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
78×cbrt-unprod_binary64_111 prod-exp_binary64_127
76×times-frac_binary64_84
59×associate-*l*_binary64_19
54×add-sqr-sqrt_binary64_100
51×*-un-lft-identity_binary64_78
49×add-cube-cbrt_binary64_113
47×associate-*l/_binary64_21
37×cbrt-undiv_binary64_112 div-exp_binary64_129
35×frac-times_binary64_88
34×pow1_binary64_139
20×pow-prod-down_binary64_149
16×tan-quot_binary64_237
15×associate-*r/_binary64_20
11×associate-*r*_binary64_18
8×flip-+_binary64_52 flip3-+_binary64_81
5×div-inv_binary64_75
4×*-commutative_binary64_9 add-log-exp_binary64_117
2×unswap-sqr_binary64_46
1×distribute-lft-in_binary64_27 distribute-rgt-in_binary64_28 associate-/r/_binary64_24 distribute-lft-out_binary64_29
Counts
4 → 214
Calls

4 calls:

33.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
17.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
17.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series689.0ms (5%)

Counts
4 → 12
Calls

4 calls:

393.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
175.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
66.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
54.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify105.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
226 → 226
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049795442
149795442

prune350.0ms (2.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New2206226
Fresh5813
Picked101
Done000
Total22614240
Error
7.8b
Counts
240 → 14
Compiler

Compiled 7205 to 3413 computations (52.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.0b
(*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
3.3b
(*.f64 (/.f64 t l) (sin.f64 k))
8.1b
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))) (*.f64 (/.f64 l t) (cos.f64 k)))
12.0b
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))

rewrite88.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
142×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
79×cbrt-unprod_binary64_111 prod-exp_binary64_127
30×cbrt-undiv_binary64_112 div-exp_binary64_129
29×pow1_binary64_139
20×associate-*l*_binary64_19
19×add-sqr-sqrt_binary64_100
17×pow-prod-down_binary64_149
16×associate-*r/_binary64_20 *-un-lft-identity_binary64_78
14×add-cube-cbrt_binary64_113
13×associate-*l/_binary64_21
11×times-frac_binary64_84
5×associate-*r*_binary64_18 associate-/l/_binary64_25
4×add-log-exp_binary64_117 flip-+_binary64_52 frac-times_binary64_88 flip3-+_binary64_81
3×*-commutative_binary64_9
2×div-inv_binary64_75 unswap-sqr_binary64_46
1×frac-2neg_binary64_89 associate-/l*_binary64_23 associate-/r*_binary64_22 associate-/r/_binary64_24 clear-num_binary64_77 distribute-lft-out_binary64_29
Counts
4 → 143
Calls

4 calls:

27.0ms
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))) (*.f64 (/.f64 l t) (cos.f64 k)))
21.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))
11.0ms
(*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
8.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series603.0ms (4.4%)

Counts
4 → 12
Calls

4 calls:

275.0ms
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))) (*.f64 (/.f64 l t) (cos.f64 k)))
183.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))
90.0ms
(*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
54.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify80.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
055554174

prune204.0ms (1.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1478155
Fresh6713
Picked101
Done000
Total15415169
Error
5.1b
Counts
169 → 15
Compiler

Compiled 5020 to 2253 computations (55.1% saved)

regimes1.6s (11.4%)

Accuracy

Total 6.5b remaining (59.6%)

Threshold costs 0b (0%)

Compiler

Compiled 15443 to 11482 computations (25.6% saved)

bsearch289.0ms (2.1%)

Steps
ItersRangePoint
8
2.880148921520459e+227
8.097579111254507e+231
3.8305734146775315e+227
7
8.247022942557457e+193
1.349953017170864e+195
1.1117120927669026e+194
8
3.5472835416240585e-81
1.0907382914714864e-77
6.597454098759182e-81
9
-1.246814367568544e-147
-7.808800158176141e-154
-1.5767169438438566e-152
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
080245
180245

end0.0ms (0%)

sample5.2s (38%)

Algorithm
1×intervals
Results
1.4s2675×body1024valid
495.0ms1287×body512valid
440.0ms3427×body128valid
191.0ms1457×body128invalid
156.0ms602×body256valid
43.0ms115×body512invalid
26.0ms105×body256invalid
24.0ms48×body1024invalid
7.0ms9×body2048valid
Compiler

Compiled 2655 to 1944 computations (26.8% saved)

Profiling

Loading profile data...