Details

Time bar (total: 10.5s)

analyze572.0ms (5.5%)

Algorithm
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
12.5%87.4%0.1%5
18.7%68.7%12.6%6
28.1%59.3%12.6%7
32.8%48.4%18.8%8
38.2%42.9%18.8%9
41%37.1%22%10
43.9%34.1%22%11
45.5%31%23.5%12
46.9%29.6%23.5%13
47.7%28%24.3%14
Compiler

Compiled 19 to 9 computations (52.6% saved)

sample72.0ms (0.7%)

Algorithm
intervals
Results
35.0ms128×body8192exit
9.0ms201×body128valid
8.0ms32×body256valid
3.0ms21×body512valid
0.0msbody1024valid
0.0msbody128invalid
Compiler

Compiled 39 to 19 computations (51.3% saved)

simplify109.0ms (1%)

Algorithm
egg-herbie
Rules
676×neg-mul-1_binary64
493×div-sub_binary64
416×distribute-neg-frac_binary64
341×distribute-rgt-neg-out_binary64
331×distribute-lft-neg-out_binary64
Counts
1 → 1
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0923
12123
25423
314421
431718
591718
6243318
7323718
8443318
9484918
10487418

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
15.2b
Counts
2 → 1
Alt Table
StatusErrorProgram
15.2b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
Compiler

Compiled 42 to 27 computations (35.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (/.f64 x (exp.f64 wj)) wj)
0.0b
(/.f64 x (exp.f64 wj))
0.0b
(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
4.6b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite134.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
14.8b
Rules
55×add-sqr-sqrt_binary64
53×*-un-lft-identity_binary64
39×times-frac_binary64
25×add-cube-cbrt_binary64
12×difference-of-squares_binary64
Counts
4 → 108
Calls

4 calls:

15.0ms
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
10.0ms
(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
7.0ms
(-.f64 (/.f64 x (exp.f64 wj)) wj)
3.0ms
(/.f64 x (exp.f64 wj))
Compiler

Compiled 2064 to 803 computations (61.1% saved)

series132.0ms (1.3%)

Error
0.1b
Counts
4 → 59
Calls

4 calls:

37.0ms
(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
30.0ms
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
18.0ms
(-.f64 (/.f64 x (exp.f64 wj)) wj)
16.0ms
(/.f64 x (exp.f64 wj))
Compiler

Compiled 1759 to 1111 computations (36.8% saved)

simplify171.0ms (1.6%)

Algorithm
egg-herbie
Rules
359×associate-*l*_binary64
355×distribute-rgt-in_binary64
296×distribute-lft-in_binary64
231×div-sub_binary64
221×associate-/l*_binary64
Counts
167 → 83
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02423279
16203169
216553139
344503139
449893139
549723139

prune47.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New81283
Fresh000
Picked011
Done000
Total81384
Error
0.0b
Counts
84 → 3
Alt Table
StatusErrorProgram
43.1b
(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
15.2b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
1.6b
(+.f64 (+.f64 x (*.f64 (+.f64 (*.f64 5/2 x) 1) (*.f64 wj wj))) (-.f64 (*.f64 x (*.f64 wj -2)) (*.f64 (+.f64 (*.f64 8/3 x) 1) (pow.f64 wj 3))))
Compiler

Compiled 1193 to 562 computations (52.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (*.f64 x (*.f64 wj -2)) (*.f64 (+.f64 (*.f64 8/3 x) 1) (pow.f64 wj 3)))
0.4b
(*.f64 8/3 x)
4.1b
(*.f64 (+.f64 (*.f64 8/3 x) 1) (pow.f64 wj 3))
7.5b
(*.f64 (+.f64 (*.f64 5/2 x) 1) (*.f64 wj wj))

rewrite111.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
21×add-sqr-sqrt_binary64
16×associate-*r*_binary64
16×add-exp-log_binary64
13×add-cbrt-cube_binary64
11×*-un-lft-identity_binary64
Counts
4 → 84
Calls

4 calls:

7.0ms
(*.f64 (+.f64 (*.f64 8/3 x) 1) (pow.f64 wj 3))
7.0ms
(*.f64 (+.f64 (*.f64 5/2 x) 1) (*.f64 wj wj))
5.0ms
(*.f64 8/3 x)
4.0ms
(-.f64 (*.f64 x (*.f64 wj -2)) (*.f64 (+.f64 (*.f64 8/3 x) 1) (pow.f64 wj 3)))
Compiler

Compiled 2654 to 1852 computations (30.2% saved)

series125.0ms (1.2%)

Error
0.0b
Counts
4 → 33
Calls

4 calls:

42.0ms
(-.f64 (*.f64 x (*.f64 wj -2)) (*.f64 (+.f64 (*.f64 8/3 x) 1) (pow.f64 wj 3)))
34.0ms
(*.f64 (+.f64 (*.f64 8/3 x) 1) (pow.f64 wj 3))
22.0ms
(*.f64 (+.f64 (*.f64 5/2 x) 1) (*.f64 wj wj))
6.0ms
(*.f64 8/3 x)
Compiler

Compiled 1919 to 1380 computations (28.1% saved)

simplify109.0ms (1%)

Algorithm
egg-herbie
Rules
579×distribute-rgt-in_binary64
561×distribute-lft-in_binary64
300×exp-prod_binary64
243×associate-*l*_binary64
229×associate-*r*_binary64
Counts
117 → 102
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01772020
14361810
215381783
345611759
451281759

prune83.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1020102
Fresh011
Picked011
Done011
Total1023105
Error
0.0b
Counts
105 → 3
Alt Table
StatusErrorProgram
43.1b
(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
15.2b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
1.6b
(+.f64 (+.f64 x (*.f64 (+.f64 (*.f64 5/2 x) 1) (*.f64 wj wj))) (-.f64 (*.f64 x (*.f64 wj -2)) (*.f64 (+.f64 (*.f64 8/3 x) 1) (pow.f64 wj 3))))
Compiler

Compiled 2151 to 1467 computations (31.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)
0.1b
(+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj)))
2.6b
(+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3))
32.3b
(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))

rewrite261.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
133×*-un-lft-identity_binary64
83×times-frac_binary64
83×add-sqr-sqrt_binary64
50×cube-prod_binary64
50×unpow-prod-down_binary64
Counts
4 → 171
Calls

4 calls:

52.0ms
(+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3))
44.0ms
(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
17.0ms
(pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)
16.0ms
(+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj)))
Compiler

Compiled 7492 to 3212 computations (57.1% saved)

series740.0ms (7.1%)

Error
0.0b
Counts
4 → 86
Calls

4 calls:

355.0ms
(/.f64 (+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)) (+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
133.0ms
(+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj)))
98.0ms
(+.f64 (pow.f64 wj 3) (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3))
85.0ms
(pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)
Compiler

Compiled 10743 to 6689 computations (37.7% saved)

simplify256.0ms (2.4%)

Algorithm
egg-herbie
Rules
329×associate-*r*_binary64
273×associate-*l*_binary64
246×associate-/l*_binary64
184×associate-/r*_binary64
174×times-frac_binary64
Counts
257 → 177
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
047314439
1152913576
2510913576

prune107.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1761177
Fresh000
Picked101
Done022
Total1773180
Error
0.0b
Counts
180 → 3
Alt Table
StatusErrorProgram
43.1b
(/.f64 (+.f64 (pow.f64 wj 3) (*.f64 (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (*.f64 wj wj) -1)) 3) (pow.f64 (-.f64 wj 1) 3))) (+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
15.2b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
1.6b
(+.f64 (+.f64 x (*.f64 (+.f64 (*.f64 5/2 x) 1) (*.f64 wj wj))) (-.f64 (*.f64 x (*.f64 wj -2)) (*.f64 (+.f64 (*.f64 8/3 x) 1) (pow.f64 wj 3))))
Compiler

Compiled 6201 to 2883 computations (53.5% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (*.f64 wj wj) -1)) 3)
0.1b
(+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj)))
2.6b
(+.f64 (pow.f64 wj 3) (*.f64 (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (*.f64 wj wj) -1)) 3) (pow.f64 (-.f64 wj 1) 3)))
32.3b
(/.f64 (+.f64 (pow.f64 wj 3) (*.f64 (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (*.f64 wj wj) -1)) 3) (pow.f64 (-.f64 wj 1) 3))) (+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))

rewrite248.0ms (2.4%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
78×add-sqr-sqrt_binary64
68×times-frac_binary64
54×*-un-lft-identity_binary64
38×add-cube-cbrt_binary64
30×cube-prod_binary64
Counts
4 → 146
Calls

4 calls:

36.0ms
(/.f64 (+.f64 (pow.f64 wj 3) (*.f64 (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (*.f64 wj wj) -1)) 3) (pow.f64 (-.f64 wj 1) 3))) (+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
25.0ms
(+.f64 (pow.f64 wj 3) (*.f64 (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (*.f64 wj wj) -1)) 3) (pow.f64 (-.f64 wj 1) 3)))
17.0ms
(pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (*.f64 wj wj) -1)) 3)
14.0ms
(+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj)))
Compiler

Compiled 8747 to 3936 computations (55% saved)

series3.2s (30.4%)

Error
0.0b
Counts
4 → 81
Calls

4 calls:

2.4s
(/.f64 (+.f64 (pow.f64 wj 3) (*.f64 (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (*.f64 wj wj) -1)) 3) (pow.f64 (-.f64 wj 1) 3))) (+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
394.0ms
(+.f64 (pow.f64 wj 3) (*.f64 (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (*.f64 wj wj) -1)) 3) (pow.f64 (-.f64 wj 1) 3)))
159.0ms
(+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj)))
69.0ms
(pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (*.f64 wj wj) -1)) 3)
Compiler

Compiled 29442 to 20711 computations (29.7% saved)

simplify372.0ms (3.6%)

Algorithm
egg-herbie
Rules
721×associate-/l*_binary64
220×+-commutative_binary64
191×*-commutative_binary64
170×sub-neg_binary64
160×associate-+r+_binary64
Counts
227 → 188
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
081622375
1292321440
2584921440

prune236.0ms (2.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1871188
Fresh000
Picked011
Done022
Total1874191
Error
0.0b
Counts
191 → 4
Alt Table
StatusErrorProgram
43.1b
(/.f64 (+.f64 (pow.f64 wj 3) (*.f64 (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 (*.f64 wj wj) -1)) 3) (pow.f64 (-.f64 wj 1) 3))) (+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
53.8b
(/.f64 (-.f64 (+.f64 (*.f64 3 (/.f64 (pow.f64 wj 5) (pow.f64 (-.f64 (*.f64 wj wj) 1) 3))) (+.f64 (/.f64 (pow.f64 wj 3) (pow.f64 (-.f64 (*.f64 wj wj) 1) 3)) (+.f64 (*.f64 9 (/.f64 (*.f64 x (pow.f64 wj 3)) (*.f64 (exp.f64 wj) (pow.f64 (-.f64 (*.f64 wj wj) 1) 3)))) (+.f64 (pow.f64 wj 3) (*.f64 3 (/.f64 (*.f64 x (pow.f64 wj 5)) (*.f64 (exp.f64 wj) (pow.f64 (-.f64 (*.f64 wj wj) 1) 3)))))))) (+.f64 (*.f64 9 (/.f64 (*.f64 x (pow.f64 wj 4)) (*.f64 (exp.f64 wj) (pow.f64 (-.f64 (*.f64 wj wj) 1) 3)))) (+.f64 (*.f64 3 (+.f64 (/.f64 (pow.f64 wj 4) (pow.f64 (-.f64 (*.f64 wj wj) 1) 3)) (/.f64 (*.f64 x (*.f64 wj wj)) (*.f64 (exp.f64 wj) (pow.f64 (-.f64 (*.f64 wj wj) 1) 3))))) (/.f64 (pow.f64 wj 6) (pow.f64 (-.f64 (*.f64 wj wj) 1) 3))))) (+.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (-.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) wj))))
15.2b
(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
1.6b
(+.f64 (+.f64 x (*.f64 (+.f64 (*.f64 5/2 x) 1) (*.f64 wj wj))) (-.f64 (*.f64 x (*.f64 wj -2)) (*.f64 (+.f64 (*.f64 8/3 x) 1) (pow.f64 wj 3))))
Compiler

Compiled 13958 to 7176 computations (48.6% saved)

regimes832.0ms (8%)

Accuracy

Total 0.5b remaining (82.3%)

Threshold costs 0.5b (82.3%)

Compiler

Compiled 14892 to 9057 computations (39.2% saved)

bsearch8.0ms (0.1%)

Compiler

Compiled 18 to 8 computations (55.6% saved)

simplify26.0ms (0.2%)

Algorithm
egg-herbie
Rules
93×distribute-rgt-neg-in_binary64
83×cancel-sign-sub-inv_binary64
67×neg-sub0_binary64
67×neg-mul-1_binary64
62×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03997
17097
29497
312197
414997
517597
621097
725197
828597
931097
1034497
1138097
1242797
1348997
1453297
1555797
1656797
1756997
1855897

end1.0ms (0%)

Compiler

Compiled 66 to 39 computations (40.9% saved)

sample2.4s (23.4%)

Algorithm
intervals
Results
1.1s3879×body8192exit
362.0ms6527×body128valid
115.0ms745×body512valid
66.0ms698×body256valid
6.0ms30×body1024valid
5.0ms83×body128invalid
0.0ms10×body128overflowed
Compiler

Compiled 343 to 207 computations (39.7% saved)

Profiling

Loading profile data...