Details

Time bar (total: 12.2s)

analyze2.1s (17.5%)

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
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%93.6%6.4%8
9.4%84.3%6.4%9
14.8%75.7%9.5%10
16%71.4%12.6%11
20.9%65.7%13.4%12
24.2%60.5%15.3%13
24.8%58.6%16.6%14
Compiler

Compiled 31 to 24 computations (22.6% saved)

sample5.1s (41.6%)

Results
2.4s2291×body1024valid
1.2s4190×body128valid
860.0ms1191×body512valid
320.0ms581×body256valid
194.0ms812×body128invalid
5.0msbody2048valid
4.0msbody1024invalid
Compiler

Compiled 92 to 71 computations (22.8% saved)

simplify53.0ms (0.4%)

Algorithm
egg-herbie
Rules
640×distribute-rgt-neg-in_binary64
474×fma-neg_binary64
418×distribute-lft-neg-in_binary64
379×div-sub_binary64
378×fma-def_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02335
14928
210028
319528
439128
5107528
6254328
7420028
8495528

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
12.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
12.6b
(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (*.f64 F F) 2) (*.f64 2 x)) (neg.f64 (/.f64 1 2)))))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 153 to 108 computations (29.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 F (sin.f64 B))
0.1b
(/.f64 x (tan.f64 B))
5.5b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
15.8b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series259.0ms (2.1%)

Counts
4 → 80
Calls

4 calls:

147.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
48.0ms
(/.f64 x (tan.f64 B))
45.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
19.0ms
(/.f64 F (sin.f64 B))

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt_binary64
31×*-un-lft-identity_binary64
31×add-cube-cbrt_binary64
30×times-frac_binary64
22×add-exp-log_binary64
Counts
4 → 123
Calls

4 calls:

7.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
3.0ms
(/.f64 x (tan.f64 B))
2.0ms
(/.f64 F (sin.f64 B))
2.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

simplify168.0ms (1.4%)

Algorithm
egg-herbie
Rules
302×fma-def_binary64
223×*-commutative_binary64
221×associate-*r*_binary64
218×fma-neg_binary64
202×+-commutative_binary64
Counts
203 → 271
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05005883
113605603
245185575
349845575
449325575

prune367.0ms (3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New25813271
Fresh101
Picked101
Done000
Total26013273
Error
0.0b
Counts
273 → 13
Alt Table
StatusErrorProgram
11.6b
(-.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) 1) (*.f64 (/.f64 (cbrt.f64 F) (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
34.0b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 1 (/.f64 (tan.f64 B) x)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
32.0b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
37.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (*.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)) (sqrt.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))) (/.f64 x (tan.f64 B)))
13.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (tan.f64 B)))))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
13.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
Compiler

Compiled 10471 to 5862 computations (44% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 x (tan.f64 B))
0.3b
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
0.4b
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
15.8b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series230.0ms (1.9%)

Counts
2 → 44
Calls

2 calls:

153.0ms
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
76.0ms
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
17×add-exp-log_binary64
12×add-sqr-sqrt_binary64
add-cbrt-cube_binary64
associate-*r*_binary64
*-un-lft-identity_binary64
Counts
2 → 52
Calls

2 calls:

5.0ms
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
4.0ms
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

simplify165.0ms (1.3%)

Algorithm
egg-herbie
Rules
829×fma-def_binary64
324×cancel-sign-sub-inv_binary64
258×sub-neg_binary64
210×fma-neg_binary64
171×associate-*r*_binary64
Counts
96 → 153
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02983456
18193211
228793191
348063191
449733191
549423191

prune384.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2682270
Fresh3912
Picked101
Done000
Total27211283
Error
0.0b
Counts
283 → 11
Alt Table
StatusErrorProgram
32.0b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
34.0b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
37.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 1 (/.f64 (tan.f64 B) x)))
10.7b
(-.f64 (/.f64 (*.f64 F (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (sin.f64 B)) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
13.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (tan.f64 B)))))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
13.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
Compiler

Compiled 10658 to 6469 computations (39.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
0.3b
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
0.4b
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
15.8b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series27.0ms (0.2%)

Counts
1 → 4
Calls

1 calls:

26.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

rewrite5.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
associate-/r*_binary64
*-un-lft-identity_binary64
times-frac_binary64
Counts
1 → 23
Calls

1 calls:

4.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

simplify87.0ms (0.7%)

Algorithm
egg-herbie
Rules
486×fma-def_binary64
400×*-commutative_binary64
387×associate-/l*_binary64
366×distribute-rgt-neg-in_binary64
328×cancel-sign-sub-inv_binary64
Counts
27 → 35
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
072458
1182387
2593380
32237378
43591378
54379378
64991378
74921378

prune362.0ms (3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2631264
Fresh1910
Picked011
Done000
Total26411275
Error
0.0b
Counts
275 → 11
Alt Table
StatusErrorProgram
32.0b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
34.0b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
37.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 1 (/.f64 (tan.f64 B) x)))
10.7b
(-.f64 (/.f64 (*.f64 F (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (sin.f64 B)) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
11.4b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 (*.f64 (cos.f64 B) (/.f64 x (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B))))) (cbrt.f64 (sin.f64 B))))
13.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (tan.f64 B)))))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 11240 to 6376 computations (43.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 x (tan.f64 B))
0.2b
(*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B)))
0.4b
(/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))
15.8b
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2)

series342.0ms (2.8%)

Counts
3 → 80
Calls

3 calls:

150.0ms
(*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B)))
146.0ms
(/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))
45.0ms
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2)

rewrite25.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt_binary64
45×times-frac_binary64
36×*-un-lft-identity_binary64
36×add-cube-cbrt_binary64
25×associate-*r*_binary64
Counts
3 → 116
Calls

3 calls:

9.0ms
(*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B)))
5.0ms
(/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))
2.0ms
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2)

simplify170.0ms (1.4%)

Algorithm
egg-herbie
Rules
347×fma-def_binary64
295×fma-neg_binary64
245×associate-*r*_binary64
228×associate-/l*_binary64
215×associate-/r*_binary64
Counts
196 → 268
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05327772
114827320
249837320
351997320

prune433.0ms (3.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New3072309
Fresh189
Picked011
Done011
Total30812320
Error
0.0b
Counts
320 → 12
Alt Table
StatusErrorProgram
32.4b
(-.f64 (*.f64 F (/.f64 -1 (*.f64 (sin.f64 B) F))) (/.f64 x (tan.f64 B)))
32.0b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
34.4b
(-.f64 (*.f64 F (/.f64 (/.f64 1 F) (sin.f64 B))) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (/.f64 (*.f64 F (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (sin.f64 B)) (/.f64 x (tan.f64 B)))
34.0b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 1 (/.f64 (tan.f64 B) x)))
10.7b
(-.f64 (*.f64 F (/.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/2) (sin.f64 B))) (/.f64 x (tan.f64 B)))
10.7b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
11.4b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 (*.f64 (cos.f64 B) (/.f64 x (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B))))) (cbrt.f64 (sin.f64 B))))
13.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (tan.f64 B)))))
12.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 12504 to 7474 computations (40.2% saved)

regimes1.5s (12.3%)

Accuracy

Total 0.2b remaining (84%)

Threshold costs 0.2b (84%)

Counts
223 → 3
Compiler

Compiled 23744 to 16048 computations (32.4% saved)

bsearch76.0ms (0.6%)

Steps
ItersRangePoint
1
6.394693602722866e+53
4.294346038226625e+54
1.586277459668285e+54
5
-2.1894104490516903e+105
-7.112557422472202e+102
-1.69148055696647e+103
Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (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
03173
14073
25173
36473
47273
57673
67773
77673

end225.0ms (1.8%)

Compiler

Compiled 390 to 248 computations (36.4% saved)

Profiling

Loading profile data...