Details

Time bar (total: 4.0s)

sample310.0ms

Algorithm
intervals
Results
24.0ms51×body1280valid
10.0ms35×body640valid
8.0ms134×body80valid
4.0ms20×body320valid
2.0ms16×body160valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0139
1219
2269
3349
4379
5379

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b
(- 1.0 (* (tan x) (tan x)))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×pow1
12×times-frac
10×add-exp-log add-cbrt-cube
8×tan-quot
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×difference-of-squares
4×associate-/l*
3×associate-/r*
2×pow2 frac-times flip3-- pow-plus associate-*r/ pow-prod-down associate-*l/ prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod associate-/l/ unswap-sqr
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-sub div-exp clear-num flip-+ div-inv
Counts
4 → 105
Calls
4 calls:
8.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms
(- 1.0 (* (tan x) (tan x)))
5.0ms
(* (tan x) (tan x))
8.0ms
(* (tan x) (tan x))

series223.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
39.0ms
(- 1.0 (* (tan x) (tan x)))
32.0ms
(* (tan x) (tan x))
60.0ms
(* (tan x) (tan x))

simplify44.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0314909
11157838
25001824

prune244.0ms

Filtered
117 candidates to 77 candidates (65.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 2)
0.3b
(pow (cos x) 2)
0.3b
(pow (sin x) 2)
0.3b
(pow (sin x) 2)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down pow-unpow *-un-lft-identity
8×pow1 add-exp-log
4×pow-to-exp pow-pow pow-exp add-cbrt-cube unpow2 add-log-exp sqr-pow
Counts
4 → 72
Calls
4 calls:
1.0ms
(pow (cos x) 2)
1.0ms
(pow (cos x) 2)
1.0ms
(pow (sin x) 2)
2.0ms
(pow (sin x) 2)

series70.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(pow (cos x) 2)
16.0ms
(pow (cos x) 2)
18.0ms
(pow (sin x) 2)
19.0ms
(pow (sin x) 2)

simplify60.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (56.0ms)

IterNodesCost
0141284
1469240
21590240
35001236

prune217.0ms

Filtered
84 candidates to 48 candidates (57.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(- 1.0 (cbrt (pow (tan x) 6)))
0.3b
(* (tan x) (tan x))
0.7b
(pow (tan x) 6)
7.9b
(cbrt (pow (tan x) 6))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
14×*-un-lft-identity
12×pow1 add-cube-cbrt
10×cbrt-prod
7×add-exp-log unpow-prod-down
6×add-cbrt-cube add-log-exp
4×tan-quot difference-of-squares
3×pow-unpow swap-sqr associate-*r* associate-*l* sqr-pow
1×pow2 frac-times pow-to-exp sub-neg flip3-- pow-pow pow-plus pow1/3 diff-log associate-*r/ pow-prod-down associate-*l/ pow-exp prod-exp pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 77
Calls
4 calls:
6.0ms
(- 1.0 (cbrt (pow (tan x) 6)))
5.0ms
(* (tan x) (tan x))
2.0ms
(pow (tan x) 6)
1.0ms
(cbrt (pow (tan x) 6))

series156.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- 1.0 (cbrt (pow (tan x) 6)))
31.0ms
(* (tan x) (tan x))
61.0ms
(pow (tan x) 6)
32.0ms
(cbrt (pow (tan x) 6))

simplify41.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0262439
11007393
25001359

prune217.0ms

Filtered
89 candidates to 56 candidates (62.9%)
Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.4b
(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
25×pow1
18×*-un-lft-identity
16×add-cube-cbrt
12×tan-quot
10×add-exp-log add-cbrt-cube
9×swap-sqr associate-*r* associate-*l*
6×add-log-exp
4×times-frac associate-/r/ difference-of-squares
3×pow2 frac-times distribute-rgt-out-- pow-plus associate-*r/ pow-prod-down associate-*l/ prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
2×flip3-+ flip-+ div-inv
1×sub-neg flip3-- diff-log frac-sub flip-- distribute-lft-out-- sub-div
Counts
4 → 106
Calls
4 calls:
5.0ms
(* (tan x) (tan x))
5.0ms
(* (tan x) (tan x))
5.0ms
(* (tan x) (tan x))
31.0ms
(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series254.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (tan x) (tan x))
32.0ms
(* (tan x) (tan x))
32.0ms
(* (tan x) (tan x))
154.0ms
(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify37.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0266869
1914800
25002784

prune210.0ms

Filtered
118 candidates to 69 candidates (58.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes184.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01616
11616

end0.0ms

sample1.6s

Algorithm
intervals
Results
706.0ms1566×body1280valid
354.0ms1246×body640valid
266.0ms4289×body80valid
115.0ms595×body320valid
42.0ms304×body160valid