Details

Time bar (total: 6.8s)

analyze775.0ms (11.4%)

Algorithm
1×search
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)

sample73.0ms (1.1%)

Algorithm
1×intervals
Results
34.0ms66×body1024valid
14.0ms137×body128valid
10.0ms33×body512valid
7.0ms20×body256valid
Compiler

Compiled 33 to 30 computations (9.1% saved)

simplify177.0ms (2.6%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
05022
15022

prune10.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 14.4b

Counts
2 → 1
Compiler

Compiled 58 to 50 computations (13.8% saved)

localize10.0ms (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)))
14.2b
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))

rewrite28.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
19×add-exp-log_binary64_16285 add-cbrt-cube_binary64_16283
10×pow1_binary64_16308 add-sqr-sqrt_binary64_16269
8×*-un-lft-identity_binary64_16247 add-cube-cbrt_binary64_16282
7×cbrt-unprod_binary64_16280 prod-exp_binary64_16296
6×associate-*l*_binary64_16188
4×pow-prod-down_binary64_16318 associate-*r*_binary64_16187
3×add-log-exp_binary64_16286 times-frac_binary64_16253 div-exp_binary64_16298 associate-/r*_binary64_16191 cbrt-undiv_binary64_16281
2×*-commutative_binary64_16178
1×clear-num_binary64_16246 associate-/l*_binary64_16192 frac-2neg_binary64_16258 unswap-sqr_binary64_16215 div-inv_binary64_16244
Counts
3 → 59
Calls

3 calls:

10.0ms
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))
8.0ms
(*.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)))

series204.0ms (3%)

Counts
3 → 9
Calls

3 calls:

115.0ms
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))
57.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 8/3 (sin.f64 (*.f64 x 1/2))))
32.0ms
(*.f64 8/3 (sin.f64 (*.f64 x 1/2)))

simplify86.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
049181066
149181066

prune482.0ms (7.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New541468
Fresh000
Picked101
Done000
Total551469

Merged error: 0.1b

Counts
69 → 14
Compiler

Compiled 7046 to 5745 computations (18.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite31.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
19×add-exp-log_binary64_16285 add-cbrt-cube_binary64_16283
14×add-sqr-sqrt_binary64_16269
10×*-un-lft-identity_binary64_16247 add-cube-cbrt_binary64_16282 associate-*r*_binary64_16187
7×pow1_binary64_16308
6×cbrt-unprod_binary64_16280 times-frac_binary64_16253 prod-exp_binary64_16296 associate-*l*_binary64_16188
4×div-exp_binary64_16298 cbrt-undiv_binary64_16281
3×add-log-exp_binary64_16286 associate-/r*_binary64_16191
2×pow-prod-down_binary64_16318 unswap-sqr_binary64_16215 *-commutative_binary64_16178 div-inv_binary64_16244
1×clear-num_binary64_16246 associate-/l*_binary64_16192 frac-2neg_binary64_16258 associate-*r/_binary64_16189
Counts
3 → 66
Calls

3 calls:

13.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) 8/3) (sin.f64 x)))
6.0ms
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) 8/3) (sin.f64 x))
5.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) 8/3)

series227.0ms (3.3%)

Counts
3 → 9
Calls

3 calls:

113.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) 8/3) (sin.f64 x)))
84.0ms
(/.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) 8/3) (sin.f64 x))
29.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) 8/3)

simplify70.0ms (1%)

Algorithm
1×egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049291245
149291245

prune411.0ms (6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New67875
Fresh7613
Picked011
Done000
Total741589

Merged error: 0.0b

Counts
89 → 15
Compiler

Compiled 6231 to 5046 computations (19% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))
0.2b
(*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
0.3b
(/.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))
0.4b
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x)))

rewrite49.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
34×add-exp-log_binary64_16285 add-cbrt-cube_binary64_16283
20×add-sqr-sqrt_binary64_16269
19×associate-*r*_binary64_16187
14×cbrt-unprod_binary64_16280 prod-exp_binary64_16296 *-un-lft-identity_binary64_16247 add-cube-cbrt_binary64_16282
13×pow1_binary64_16308
7×sqrt-prod_binary64_16263 associate-*l*_binary64_16188
6×times-frac_binary64_16253 div-exp_binary64_16298 cbrt-undiv_binary64_16281
5×pow-prod-down_binary64_16318
4×add-log-exp_binary64_16286
3×unswap-sqr_binary64_16215 *-commutative_binary64_16178 associate-/r*_binary64_16191
2×div-inv_binary64_16244
1×clear-num_binary64_16246 associate-/l*_binary64_16192 frac-2neg_binary64_16258 associate-*r/_binary64_16189
Counts
4 → 95
Calls

4 calls:

13.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x)))
10.0ms
(/.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))
9.0ms
(*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
7.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))

series471.0ms (6.9%)

Counts
4 → 12
Calls

4 calls:

194.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x)))
157.0ms
(/.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))
70.0ms
(*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
49.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))

simplify78.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049051758
149051758

prune277.0ms (4.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1043107
Fresh7613
Picked011
Done011
Total11111122

Merged error: 0.0b

Counts
122 → 11
Compiler

Compiled 4251 to 3420 computations (19.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 1 (sin.f64 x))
0.2b
(*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
0.4b
(*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (/.f64 1 (sin.f64 x))))
0.4b
(*.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (/.f64 1 (sin.f64 x)))

rewrite66.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
105×add-exp-log_binary64_16285
64×prod-exp_binary64_16296
61×add-cbrt-cube_binary64_16283
34×cbrt-unprod_binary64_16280
33×pow1_binary64_16308
22×add-sqr-sqrt_binary64_16269 *-un-lft-identity_binary64_16247 add-cube-cbrt_binary64_16282
20×associate-*r*_binary64_16187
19×pow-prod-down_binary64_16318
18×times-frac_binary64_16253
14×div-exp_binary64_16298
7×1-exp_binary64_16291 rec-exp_binary64_16297 cbrt-undiv_binary64_16281
5×associate-*l*_binary64_16188
4×add-log-exp_binary64_16286 associate-*r/_binary64_16189
3×sqrt-prod_binary64_16263 associate-/l*_binary64_16192 *-commutative_binary64_16178 associate-/r*_binary64_16191
2×un-div-inv_binary64_16245 div-inv_binary64_16244
1×clear-num_binary64_16246 pow-flip_binary64_16321 frac-2neg_binary64_16258 inv-pow_binary64_16332
Counts
4 → 135
Calls

4 calls:

18.0ms
(*.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (/.f64 1 (sin.f64 x)))
18.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (/.f64 1 (sin.f64 x))))
9.0ms
(*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
4.0ms
(/.f64 1 (sin.f64 x))

series504.0ms (7.4%)

Counts
4 → 12
Calls

4 calls:

196.0ms
(*.f64 (sin.f64 (*.f64 x 1/2)) (*.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (/.f64 1 (sin.f64 x))))
159.0ms
(*.f64 (*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (/.f64 1 (sin.f64 x)))
104.0ms
(*.f64 (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
44.0ms
(/.f64 1 (sin.f64 x))

simplify86.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049132166
149132166

prune174.0ms (2.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1470147
Fresh088
Picked011
Done022
Total14711158

Merged error: 0.0b

Counts
158 → 11
Compiler

Compiled 2848 to 2170 computations (23.8% saved)

regimes28.0ms (0.4%)

Compiler

Compiled 217 to 184 computations (15.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01629
11629

end0.0ms (0%)

sample2.4s (36%)

Algorithm
1×intervals
Results
1.1s2009×body1024valid
464.0ms4497×body128valid
315.0ms990×body512valid
104.0ms499×body256valid
6.0ms5×body2048valid
Compiler

Compiled 266 to 228 computations (14.3% saved)

Profiling

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