Details

Time bar (total: 19.5s)

analyze1.6s (8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
1.8%98%0.2%10
7.7%92.1%0.2%11
10.4%89.4%0.2%12
12.1%87.7%0.2%13
21.4%78.3%0.4%14
Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.7s (8.7%)

Results
931.0ms6908×body128valid
216.0ms435×body1024valid
180.0ms490×body512valid
161.0ms1253×body128invalid
102.0ms367×body256valid
25.0ms56×body2048valid
Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify81.0ms (0.4%)

Algorithm
egg-herbie
Rules
930×fma-def_binary64
859×div-sub_binary64
817×unsub-neg_binary64
555×neg-mul-1_binary64
380×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01219
12417
25217
315517
447717
5126817
6321317
7415417
8443417
9496517
10495117

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
17.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
17.2b
(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
17.2b
(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
Compiler

Compiled 100 to 54 computations (46% saved)

localize9.0ms (0%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 t x) (-.f64 a z))
17.1b
(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series102.0ms (0.5%)

Counts
2 → 108
Calls

2 calls:

73.0ms
(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
29.0ms
(/.f64 (-.f64 t x) (-.f64 a z))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity_binary64
38×add-sqr-sqrt_binary64
25×times-frac_binary64
14×add-cube-cbrt_binary64
12×distribute-lft-out--_binary64
Counts
2 → 64
Calls

2 calls:

6.0ms
(/.f64 (-.f64 t x) (-.f64 a z))
0.0ms
(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

simplify122.0ms (0.6%)

Algorithm
egg-herbie
Rules
523×cancel-sign-sub-inv_binary64
479×sub-neg_binary64
353×associate-+r+_binary64
286×+-commutative_binary64
272×associate-+l+_binary64
Counts
172 → 136
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03566269
110456192
238516156
352336156

prune112.0ms (0.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1279136
Fresh011
Picked101
Done000
Total12810138
Error
1.2b
Counts
138 → 10
Alt Table
StatusErrorProgram
17.8b
(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)
37.4b
(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (+.f64 t (/.f64 (*.f64 a t) z))) (+.f64 (/.f64 (*.f64 y t) z) (/.f64 (*.f64 a x) z)))
40.5b
(fma.f64 (-.f64 y z) (*.f64 (sqrt.f64 (-.f64 t x)) (/.f64 (sqrt.f64 (-.f64 t x)) (-.f64 a z))) x)
17.2b
(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
32.0b
(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
35.7b
(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
17.3b
(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
17.8b
(-.f64 (+.f64 (/.f64 (*.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (*.f64 y x) (-.f64 a z)) (/.f64 (*.f64 t z) (-.f64 a z))))
38.0b
(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
39.4b
(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
Compiler

Compiled 4898 to 1542 computations (68.5% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 t x) (-.f64 a z))
3.9b
(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
8.1b
(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

series196.0ms (1%)

Counts
2 → 120
Calls

2 calls:

103.0ms
(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
92.0ms
(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

rewrite26.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt_binary64
37×*-un-lft-identity_binary64
31×associate-*r*_binary64
26×times-frac_binary64
15×add-cube-cbrt_binary64
Counts
2 → 74
Calls

2 calls:

13.0ms
(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
3.0ms
(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

simplify156.0ms (0.8%)

Algorithm
egg-herbie
Rules
426×associate-+l+_binary64
315×fma-neg_binary64
251×associate--l+_binary64
240×associate-/l*_binary64
230×associate--r+_binary64
Counts
194 → 181
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04488843
113508780
247418780
350208780

prune203.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2435248
Fresh459
Picked101
Done000
Total24810258
Error
1.2b
Counts
258 → 10
Alt Table
StatusErrorProgram
35.7b
(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
17.8b
(+.f64 x (*.f64 (*.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))))
39.3b
(+.f64 x (/.f64 (*.f64 (-.f64 (*.f64 y y) (*.f64 z z)) (-.f64 t x)) (*.f64 (+.f64 y z) (-.f64 a z))))
37.4b
(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (+.f64 t (/.f64 (*.f64 a t) z))) (+.f64 (/.f64 (*.f64 y t) z) (/.f64 (*.f64 a x) z)))
32.0b
(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
22.6b
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
17.3b
(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
36.4b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))) (-.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))))
17.2b
(+.f64 x (*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))))
38.0b
(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
Compiler

Compiled 9232 to 2771 computations (70% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 x (-.f64 a z))
0.0b
(-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))
4.1b
(+.f64 x (*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))))
8.1b
(*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))

series225.0ms (1.2%)

Counts
4 → 174
Calls

4 calls:

100.0ms
(+.f64 x (*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))))
74.0ms
(*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
35.0ms
(-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))
16.0ms
(/.f64 x (-.f64 a z))

rewrite1.1s (5.6%)

Algorithm
rewrite-expression-head
Rules
3323×*-un-lft-identity_binary64
3305×add-sqr-sqrt_binary64
3291×times-frac_binary64
2205×prod-diff_binary64
1965×add-cube-cbrt_binary64
Counts
4 → 2471
Calls

4 calls:

66.0ms
(+.f64 x (*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))))
55.0ms
(*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
29.0ms
(-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))
12.0ms
(/.f64 x (-.f64 a z))

simplify3.5s (18%)

Algorithm
egg-herbie
Rules
785×+-commutative_binary64
637×fma-def_binary64
471×*-commutative_binary64
338×times-frac_binary64
307×fma-udef_binary64
Counts
2645 → 3014
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02219175695
13800163403
24615162751
35052162751

prune2.6s (13.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New300863014
Fresh369
Picked101
Done000
Total3012123024
Error
1.2b
Counts
3024 → 12
Alt Table
StatusErrorProgram
39.3b
(+.f64 x (/.f64 (*.f64 (-.f64 (*.f64 y y) (*.f64 z z)) (-.f64 t x)) (*.f64 (+.f64 y z) (-.f64 a z))))
37.4b
(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (+.f64 t (/.f64 (*.f64 a t) z))) (+.f64 (/.f64 (*.f64 y t) z) (/.f64 (*.f64 a x) z)))
45.8b
(+.f64 (+.f64 x (*.f64 (fma.f64 1 (/.f64 t (-.f64 a z)) (neg.f64 (*.f64 (+.f64 (*.f64 a a) (+.f64 (*.f64 z z) (*.f64 a z))) (/.f64 x (-.f64 (pow.f64 a 3) (pow.f64 z 3)))))) (-.f64 y z))) (*.f64 (fma.f64 (neg.f64 (+.f64 (*.f64 a a) (+.f64 (*.f64 z z) (*.f64 a z)))) (/.f64 x (-.f64 (pow.f64 a 3) (pow.f64 z 3))) (*.f64 (+.f64 (*.f64 a a) (+.f64 (*.f64 z z) (*.f64 a z))) (/.f64 x (-.f64 (pow.f64 a 3) (pow.f64 z 3))))) (-.f64 y z)))
32.0b
(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
33.4b
(+.f64 (+.f64 x (*.f64 (fma.f64 1 (/.f64 t (-.f64 a z)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 x (-.f64 a z))) (sqrt.f64 (/.f64 x (-.f64 a z)))))) (-.f64 y z))) (*.f64 (fma.f64 (neg.f64 (sqrt.f64 (/.f64 x (-.f64 a z)))) (sqrt.f64 (/.f64 x (-.f64 a z))) (*.f64 (sqrt.f64 (/.f64 x (-.f64 a z))) (sqrt.f64 (/.f64 x (-.f64 a z))))) (-.f64 y z)))
36.4b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))) (-.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))))
17.2b
(+.f64 (fma.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (*.f64 x (/.f64 1 (-.f64 a z)))) x) (*.f64 (fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) x (*.f64 (/.f64 1 (-.f64 a z)) x)) (-.f64 y z)))
17.8b
(+.f64 x (*.f64 (*.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))))
22.6b
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
41.7b
(+.f64 (fma.f64 (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))) (-.f64 y z) x) (*.f64 (fma.f64 (neg.f64 (/.f64 (sqrt.f64 x) (-.f64 a z))) (/.f64 (sqrt.f64 x) 1) (*.f64 (/.f64 (sqrt.f64 x) (-.f64 a z)) (/.f64 (sqrt.f64 x) 1))) (-.f64 y z)))
17.3b
(+.f64 x (*.f64 (-.f64 y z) (fma.f64 t (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 x (-.f64 a z))))))
38.0b
(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
Compiler

Compiled 196827 to 31097 computations (84.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 x (/.f64 1 (-.f64 a z)))
0.2b
(*.f64 (/.f64 1 (-.f64 a z)) x)
17.1b
(fma.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (*.f64 x (/.f64 1 (-.f64 a z)))) x)
45.6b
(fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) x (*.f64 (/.f64 1 (-.f64 a z)) x))

series471.0ms (2.4%)

Counts
4 → 168
Calls

4 calls:

360.0ms
(fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) x (*.f64 (/.f64 1 (-.f64 a z)) x))
74.0ms
(fma.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (*.f64 x (/.f64 1 (-.f64 a z)))) x)
19.0ms
(*.f64 (/.f64 1 (-.f64 a z)) x)
17.0ms
(*.f64 x (/.f64 1 (-.f64 a z)))

rewrite24.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt_binary64
38×*-un-lft-identity_binary64
34×times-frac_binary64
24×associate-*r*_binary64
24×associate-*l*_binary64
Counts
4 → 111
Calls

4 calls:

9.0ms
(*.f64 x (/.f64 1 (-.f64 a z)))
8.0ms
(*.f64 (/.f64 1 (-.f64 a z)) x)
0.0ms
(fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) x (*.f64 (/.f64 1 (-.f64 a z)) x))
0.0ms
(fma.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (*.f64 x (/.f64 1 (-.f64 a z)))) x)

simplify133.0ms (0.7%)

Algorithm
egg-herbie
Rules
386×cancel-sign-sub-inv_binary64
351×sub-neg_binary64
338×associate-+r+_binary64
261×+-commutative_binary64
256×distribute-neg-in_binary64
Counts
279 → 224
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03596531
19626323
236086277
350126277

prune323.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2231224
Fresh01111
Picked101
Done000
Total22412236
Error
1.2b
Counts
236 → 12
Alt Table
StatusErrorProgram
39.3b
(+.f64 x (/.f64 (*.f64 (-.f64 (*.f64 y y) (*.f64 z z)) (-.f64 t x)) (*.f64 (+.f64 y z) (-.f64 a z))))
37.4b
(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (+.f64 t (/.f64 (*.f64 a t) z))) (+.f64 (/.f64 (*.f64 y t) z) (/.f64 (*.f64 a x) z)))
45.8b
(+.f64 (+.f64 x (*.f64 (fma.f64 1 (/.f64 t (-.f64 a z)) (neg.f64 (*.f64 (+.f64 (*.f64 a a) (+.f64 (*.f64 z z) (*.f64 a z))) (/.f64 x (-.f64 (pow.f64 a 3) (pow.f64 z 3)))))) (-.f64 y z))) (*.f64 (fma.f64 (neg.f64 (+.f64 (*.f64 a a) (+.f64 (*.f64 z z) (*.f64 a z)))) (/.f64 x (-.f64 (pow.f64 a 3) (pow.f64 z 3))) (*.f64 (+.f64 (*.f64 a a) (+.f64 (*.f64 z z) (*.f64 a z))) (/.f64 x (-.f64 (pow.f64 a 3) (pow.f64 z 3))))) (-.f64 y z)))
32.0b
(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
33.4b
(+.f64 (+.f64 x (*.f64 (fma.f64 1 (/.f64 t (-.f64 a z)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 x (-.f64 a z))) (sqrt.f64 (/.f64 x (-.f64 a z)))))) (-.f64 y z))) (*.f64 (fma.f64 (neg.f64 (sqrt.f64 (/.f64 x (-.f64 a z)))) (sqrt.f64 (/.f64 x (-.f64 a z))) (*.f64 (sqrt.f64 (/.f64 x (-.f64 a z))) (sqrt.f64 (/.f64 x (-.f64 a z))))) (-.f64 y z)))
36.4b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))) (-.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))))
17.8b
(+.f64 x (*.f64 (*.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))))
22.6b
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
41.7b
(+.f64 (fma.f64 (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))) (-.f64 y z) x) (*.f64 (fma.f64 (neg.f64 (/.f64 (sqrt.f64 x) (-.f64 a z))) (/.f64 (sqrt.f64 x) 1) (*.f64 (/.f64 (sqrt.f64 x) (-.f64 a z)) (/.f64 (sqrt.f64 x) 1))) (-.f64 y z)))
21.5b
(+.f64 (fma.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (*.f64 x (/.f64 1 (-.f64 a z)))) x) (*.f64 (expm1.f64 (log1p.f64 (fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) x (*.f64 (/.f64 1 (-.f64 a z)) x)))) (-.f64 y z)))
17.3b
(+.f64 x (*.f64 (-.f64 y z) (fma.f64 t (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 x (-.f64 a z))))))
38.0b
(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
Compiler

Compiled 11830 to 4379 computations (63% saved)

regimes6.5s (33.6%)

Accuracy

Total 3.8b remaining (79.4%)

Threshold costs 0b (0%)

Counts
303 → 6
Compiler

Compiled 58726 to 30064 computations (48.8% saved)

bsearch15.0ms (0.1%)

Compiler

Compiled 18 to 11 computations (38.9% saved)

simplify14.0ms (0.1%)

Algorithm
egg-herbie
Rules
27×+-commutative_binary64
22×*-commutative_binary64
20×sub-neg_binary64
15×neg-sub0_binary64
15×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050342
173342
295342
3123342
4162342
5180342
6190342
7193342
8193342

end227.0ms (1.2%)

Compiler

Compiled 931 to 311 computations (66.6% saved)

Profiling

Loading profile data...