Details

Time bar (total: 8.5s)

analyze878.0ms (10.3%)

Algorithm
1×search
2×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05022
15022
011
111
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
37.5%62.5%0%4
43.7%56.2%0%5
46.9%53.1%0%6
48.4%51.5%0%7
49.2%50.8%0%8
49.6%50.4%0%9
49.8%50.2%0%10
49.9%50.1%0%11
49.9%50%0%12
50%50%0%13
50%49.9%0%14
Compiler

Compiled 17 to 15 computations (11.8% saved)

sample62.0ms (0.7%)

Algorithm
1×intervals
Results
22.0ms55×body1024valid
13.0ms138×body128valid
12.0ms42×body512valid
4.0ms21×body256valid
Compiler

Compiled 33 to 30 computations (9.1% saved)

simplify9.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
05022
15022

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
15.6b
Counts
2 → 1
Compiler

Compiled 28 to 24 computations (14.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b
(*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))
0.4b
(*.f64 8/3 (sin.f64 (*.f64 x 1/2)))
15.4b
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))

rewrite125.0ms (1.5%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
19×add-exp-log_binary64_17166 add-cbrt-cube_binary64_17164
10×pow1_binary64_17189 add-sqr-sqrt_binary64_17150
8×add-cube-cbrt_binary64_17163 *-un-lft-identity_binary64_17128
7×prod-exp_binary64_17177 cbrt-unprod_binary64_17161
6×associate-*l*_binary64_17069
4×pow-prod-down_binary64_17199 associate-*r*_binary64_17068
3×div-exp_binary64_17179 add-log-exp_binary64_17167 cbrt-undiv_binary64_17162 times-frac_binary64_17134 associate-/r*_binary64_17072
2×*-commutative_binary64_17059
1×frac-2neg_binary64_17139 clear-num_binary64_17127 div-inv_binary64_17125 associate-/l*_binary64_17073 unswap-sqr_binary64_17096
Counts
3 → 59
Calls

3 calls:

9.0ms
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))
7.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))
5.0ms
(*.f64 8/3 (sin.f64 (*.f64 x 1/2)))
Compiler

Compiled 1330 to 993 computations (25.3% saved)

series172.0ms (2%)

Error
0.3b
Counts
3 → 18
Calls

3 calls:

76.0ms
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))
45.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))
31.0ms
(*.f64 8/3 (sin.f64 (*.f64 x 1/2)))
Compiler

Compiled 608 to 494 computations (18.8% saved)

simplify58.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
049101219
149101219

prune105.0ms (1.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New641377
Fresh000
Picked101
Done000
Total651378
Error
0.1b
Counts
78 → 13
Compiler

Compiled 1514 to 1151 computations (24% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.3b
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x)))
0.4b
(/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))
0.4b
(*.f64 8/3 (sin.f64 (*.f64 x 1/2)))

rewrite114.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
19×add-exp-log_binary64_17166 add-cbrt-cube_binary64_17164
14×add-sqr-sqrt_binary64_17150
10×add-cube-cbrt_binary64_17163 *-un-lft-identity_binary64_17128 associate-*r*_binary64_17068
7×pow1_binary64_17189
6×prod-exp_binary64_17177 cbrt-unprod_binary64_17161 associate-*l*_binary64_17069 times-frac_binary64_17134
4×div-exp_binary64_17179 cbrt-undiv_binary64_17162
3×add-log-exp_binary64_17167 associate-/r*_binary64_17072
2×pow-prod-down_binary64_17199 unswap-sqr_binary64_17096 *-commutative_binary64_17059 div-inv_binary64_17125
1×frac-2neg_binary64_17139 clear-num_binary64_17127 associate-/l*_binary64_17073 associate-*r/_binary64_17070
Counts
3 → 66
Calls

3 calls:

9.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x)))
5.0ms
(/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))
5.0ms
(*.f64 8/3 (sin.f64 (*.f64 x 1/2)))
Compiler

Compiled 1482 to 1080 computations (27.1% saved)

series174.0ms (2%)

Error
0.1b
Counts
3 → 18
Calls

3 calls:

71.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x)))
54.0ms
(/.f64 (*.f64 8/3 (sin.f64 (*.f64 x 1/2))) (sin.f64 x))
32.0ms
(*.f64 8/3 (sin.f64 (*.f64 x 1/2)))
Compiler

Compiled 610 to 502 computations (17.7% saved)

simplify83.0ms (1%)

Algorithm
1×egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
049081385
149081385

prune111.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New77784
Fresh5712
Picked101
Done000
Total831497
Error
0.0b
Counts
97 → 14
Compiler

Compiled 1774 to 1339 computations (24.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))
0.2b
(*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)))
0.3b
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))) (sin.f64 x)))
0.4b
(/.f64 (*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))) (sin.f64 x))

rewrite201.0ms (2.4%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
34×add-exp-log_binary64_17166 add-cbrt-cube_binary64_17164
20×add-sqr-sqrt_binary64_17150
14×prod-exp_binary64_17177 add-cube-cbrt_binary64_17163 cbrt-unprod_binary64_17161 *-un-lft-identity_binary64_17128 associate-*r*_binary64_17068
13×pow1_binary64_17189
12×associate-*l*_binary64_17069
7×sqrt-prod_binary64_17144
6×div-exp_binary64_17179 cbrt-undiv_binary64_17162 times-frac_binary64_17134
5×pow-prod-down_binary64_17199
4×add-log-exp_binary64_17167
3×associate-/r*_binary64_17072 unswap-sqr_binary64_17096 *-commutative_binary64_17059
2×div-inv_binary64_17125
1×frac-2neg_binary64_17139 clear-num_binary64_17127 associate-/l*_binary64_17073 associate-*r/_binary64_17070
Counts
4 → 95
Calls

4 calls:

12.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))) (sin.f64 x)))
12.0ms
(/.f64 (*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))) (sin.f64 x))
8.0ms
(*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)))
6.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))
Compiler

Compiled 2640 to 2092 computations (20.8% saved)

series369.0ms (4.3%)

Error
0.0b
Counts
4 → 24
Calls

4 calls:

119.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))) (sin.f64 x)))
104.0ms
(/.f64 (*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))) (sin.f64 x))
61.0ms
(*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)))
52.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))
Compiler

Compiled 1316 to 1156 computations (12.2% saved)

simplify70.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
050101959

prune154.0ms (1.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1172119
Fresh4913
Picked011
Done000
Total12112133
Error
0.0b
Counts
133 → 12
Compiler

Compiled 2565 to 1997 computations (22.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))
0.2b
(*.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x)))
0.2b
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sin.f64 x))
0.3b
(*.f64 (*.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))) (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sin.f64 x)))

rewrite200.0ms (2.3%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
34×add-exp-log_binary64_17166 add-cbrt-cube_binary64_17164
22×add-sqr-sqrt_binary64_17150
16×associate-*r*_binary64_17068
14×prod-exp_binary64_17177 add-cube-cbrt_binary64_17163 cbrt-unprod_binary64_17161 *-un-lft-identity_binary64_17128
13×pow1_binary64_17189
10×associate-*l*_binary64_17069
8×sqrt-prod_binary64_17144
6×div-exp_binary64_17179 cbrt-undiv_binary64_17162 times-frac_binary64_17134
5×pow-prod-down_binary64_17199
4×add-log-exp_binary64_17167 unswap-sqr_binary64_17096
3×*-commutative_binary64_17059 associate-/r*_binary64_17072
2×div-inv_binary64_17125
1×associate-*r/_binary64_17070 frac-2neg_binary64_17139 clear-num_binary64_17127 associate-/l*_binary64_17073
Counts
4 → 96
Calls

4 calls:

12.0ms
(*.f64 (*.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))) (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sin.f64 x)))
10.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))
7.0ms
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sin.f64 x))
6.0ms
(*.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x)))
Compiler

Compiled 2628 to 2070 computations (21.2% saved)

series327.0ms (3.8%)

Error
0.0b
Counts
4 → 24
Calls

4 calls:

114.0ms
(*.f64 (*.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x))) (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sin.f64 x)))
73.0ms
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sin.f64 x))
54.0ms
(*.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 1/2 x)))
50.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))
Compiler

Compiled 1296 to 1136 computations (12.3% saved)

simplify97.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
049202111
149202111

prune157.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1173120
Fresh2810
Picked101
Done101
Total12111132
Error
0b
Counts
132 → 11
Compiler

Compiled 2530 to 1998 computations (21% saved)

regimes639.0ms (7.5%)

Accuracy

Total 0.4b remaining (99.8%)

Threshold costs 0.4b (99.8%)

Compiler

Compiled 4600 to 3922 computations (14.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01629
11629

end0.0ms (0%)

sample4.4s (51.2%)

Algorithm
1×intervals
Results
854.0ms2004×body1024valid
460.0ms4506×body128valid
295.0ms1009×body512valid
103.0ms475×body256valid
5.0ms6×body2048valid
Compiler

Compiled 2334 to 1992 computations (14.7% saved)

Profiling

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