Details

Time bar (total: 8.5s)

analyze2.3s (27.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
3.1%96.5%0.3%9
4.7%95%0.3%10
4.7%95%0.3%11
5.1%82.1%12.8%12
6.2%74.7%19%13
6.4%74.5%19%14
Compiler

Compiled 41 to 30 computations (26.8% saved)

sample2.9s (34.3%)

Results
1.7s8256×body128valid
1.1s5150×body128invalid
Compiler

Compiled 122 to 89 computations (27% saved)

simplify46.0ms (0.5%)

Algorithm
egg-herbie
Rules
829×fma-neg_binary64
433×exp-sum_binary64
321×distribute-rgt-in_binary64
303×distribute-lft-in_binary64
279×unsub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03047
15542
213640
351240
4210640
5452040
6499240

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
3.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
3.1b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))
Compiler

Compiled 135 to 87 computations (35.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 z (sqrt.f64 (+.f64 t a)))
0.4b
(/.f64 2/3 t)
1.9b
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
5.4b
(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series143.0ms (1.7%)

Counts
4 → 88
Calls

4 calls:

63.0ms
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
44.0ms
(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
34.0ms
(*.f64 z (sqrt.f64 (+.f64 t a)))
1.0ms
(/.f64 2/3 t)

rewrite21.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64
19×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
Counts
4 → 91
Calls

4 calls:

6.0ms
(*.f64 z (sqrt.f64 (+.f64 t a)))
6.0ms
(/.f64 2/3 t)
5.0ms
(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
0.0ms
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))

simplify152.0ms (1.8%)

Algorithm
egg-herbie
Rules
801×times-frac_binary64
430×cancel-sign-sub-inv_binary64
324×fma-neg_binary64
272×sub-neg_binary64
270×fma-def_binary64
Counts
179 → 189
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03214150
18643932
229923925
348653924
449563924

prune238.0ms (2.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1863189
Fresh000
Picked101
Done000
Total1873190
Error
0b
Counts
190 → 3
Alt Table
StatusErrorProgram
17.0b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
19.1b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 c (+.f64 a 5/6) (*.f64 b (-.f64 -5/6 a)))) x))
30.6b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))
Compiler

Compiled 6983 to 3532 computations (49.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (/.f64 1 t))
0.1b
(*.f64 (sqrt.f64 (/.f64 1 t)) z)
0.4b
(/.f64 2/3 t)
0.6b
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))

series77.0ms (0.9%)

Counts
3 → 51
Calls

3 calls:

55.0ms
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))
16.0ms
(*.f64 (sqrt.f64 (/.f64 1 t)) z)
5.0ms
(sqrt.f64 (/.f64 1 t))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt_binary64
29×sqrt-prod_binary64
22×times-frac_binary64
21×*-un-lft-identity_binary64
19×add-cube-cbrt_binary64
Counts
3 → 77
Calls

3 calls:

6.0ms
(*.f64 (sqrt.f64 (/.f64 1 t)) z)
2.0ms
(sqrt.f64 (/.f64 1 t))
0.0ms
(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))

simplify92.0ms (1.1%)

Algorithm
egg-herbie
Rules
659×distribute-rgt-in_binary64
617×distribute-lft-in_binary64
462×fma-neg_binary64
279×sub-neg_binary64
268×fma-def_binary64
Counts
128 → 119
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01322796
12922685
28622514
322302438
452672438

prune171.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1511152
Fresh112
Picked011
Done000
Total1523155
Error
0b
Counts
155 → 3
Alt Table
StatusErrorProgram
17.0b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
18.8b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (-.f64 c b) (+.f64 5/6 a))) x))
30.6b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))
Compiler

Compiled 4767 to 2988 computations (37.3% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (-.f64 c b) (+.f64 5/6 a))) x)
0.0b
(+.f64 5/6 a)
0.2b
(*.f64 (-.f64 c b) (+.f64 5/6 a))

series152.0ms (1.8%)

Counts
3 → 99
Calls

3 calls:

142.0ms
(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (-.f64 c b) (+.f64 5/6 a))) x)
8.0ms
(*.f64 (-.f64 c b) (+.f64 5/6 a))
1.0ms
(+.f64 5/6 a)

rewrite14.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
add-cube-cbrt_binary64
associate-*l*_binary64
add-cbrt-cube_binary64
Counts
3 → 60
Calls

3 calls:

6.0ms
(*.f64 (-.f64 c b) (+.f64 5/6 a))
4.0ms
(+.f64 5/6 a)
0.0ms
(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (-.f64 c b) (+.f64 5/6 a))) x)

simplify116.0ms (1.4%)

Algorithm
egg-herbie
Rules
604×associate-*r*_binary64
554×cancel-sign-sub-inv_binary64
451×associate-*l*_binary64
333×fma-def_binary64
315×*-commutative_binary64
Counts
159 → 127
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03143720
110203400
239143400
353153400

prune134.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1270127
Fresh011
Picked011
Done011
Total1273130
Error
0b
Counts
130 → 3
Alt Table
StatusErrorProgram
17.0b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
18.8b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (-.f64 c b) (+.f64 5/6 a))) x))
30.6b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))
Compiler

Compiled 4310 to 2615 computations (39.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))
0.1b
(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))
0.3b
(*.f64 c -2/3)
1.8b
(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)

series84.0ms (1%)

Counts
4 → 123
Calls

4 calls:

48.0ms
(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)
21.0ms
(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))
13.0ms
(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))
2.0ms
(*.f64 c -2/3)

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt_binary64
14×*-un-lft-identity_binary64
14×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
4 → 69
Calls

4 calls:

3.0ms
(*.f64 c -2/3)
2.0ms
(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)
0.0ms
(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))
0.0ms
(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))

simplify117.0ms (1.4%)

Algorithm
egg-herbie
Rules
828×times-frac_binary64
828×fma-def_binary64
276×fma-neg_binary64
259×div-sub_binary64
225×distribute-rgt-neg-out_binary64
Counts
192 → 131
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01292934
12342721
26072648
318292528
445772528
550402528

prune118.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1310131
Fresh000
Picked011
Done022
Total1313134
Error
0b
Counts
134 → 3
Alt Table
StatusErrorProgram
17.0b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (*.f64 (sqrt.f64 (/.f64 1 t)) z))) x))
18.8b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (-.f64 c b) (+.f64 5/6 a))) x))
30.6b
(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))
Compiler

Compiled 3518 to 1945 computations (44.7% saved)

regimes1.3s (15.9%)

Accuracy

Total 1.6b remaining (96.8%)

Threshold costs 0b (0%)

Counts
81 → 1
Compiler

Compiled 27341 to 20084 computations (26.5% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
*-commutative_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02440
13140
24240
34640
44840
54740

end146.0ms (1.7%)

Compiler

Compiled 149 to 104 computations (30.2% saved)

Profiling

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