Details

Time bar (total: 17.0s)

sample190.0ms

Algorithm
intervals
Results
111.0ms137×body1280valid
30.0ms69×body640valid
12.0ms256×pre80true
7.0ms22×body320valid
2.0ms21×body80valid
2.0ms7×body160valid

simplify26.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0155
1225
2335
3395
4505
5705
6995
71245
81665
92595
102605
112605

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b
(- (tan (+ y z)) (tan a))
0.2b
(+ x (- (tan (+ y z)) (tan a)))
3.6b
(tan (+ y z))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
19×add-sqr-sqrt
18×prod-diff
17×add-cube-cbrt
11×associate-+r+
10×add-log-exp
4×tan-quot
3×pow1 add-exp-log expm1-log1p-u fma-def fma-neg add-cbrt-cube log1p-expm1-u
2×sub-neg tan-sum diff-log sum-log frac-sub distribute-lft-out distribute-lft-out--
1×+-commutative associate-+r- flip3-- flip3-+ flip-- flip-+ difference-of-squares
Counts
3 → 72
Calls
3 calls:
9.0ms
(- (tan (+ y z)) (tan a))
9.0ms
(+ x (- (tan (+ y z)) (tan a)))
4.0ms
(tan (+ y z))

series320.0ms

Counts
3 → 9
Calls
3 calls:
125.0ms
(- (tan (+ y z)) (tan a))
137.0ms
(+ x (- (tan (+ y z)) (tan a)))
57.0ms
(tan (+ y z))

simplify105.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0276685
1732540
23057507
35001488

prune260.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan y) (tan z))
0.2b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b
(* (tan y) (tan z))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
151×*-un-lft-identity
108×prod-diff
107×add-sqr-sqrt
100×add-cube-cbrt
85×times-frac
56×associate-+r+
24×distribute-lft-out
18×fma-neg
14×associate-/r/
13×add-log-exp
8×flip3-- flip--
7×tan-quot div-inv
6×pow1 add-exp-log fma-def add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×associate-*r* associate-*l* sum-log
2×+-commutative sub-neg flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times associate-+r- associate-*r/ pow-prod-down associate-*l/ frac-add prod-exp *-commutative frac-sub cbrt-unprod unswap-sqr
Counts
4 → 207
Calls
4 calls:
3.0ms
(+ (tan y) (tan z))
84.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
54.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms
(* (tan y) (tan z))

series1.0s

Counts
4 → 12
Calls
4 calls:
101.0ms
(+ (tan y) (tan z))
387.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
429.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
104.0ms
(* (tan y) (tan z))

simplify86.0ms

Algorithm
egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06764084
120873388
250013271

prune750.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
0.2b
(/ (* (tan y) (sin z)) (cos z))
0.3b
(* (tan y) (sin z))

rewrite306.0ms

Algorithm
rewrite-expression-head
Rules
321×*-un-lft-identity
237×add-sqr-sqrt
180×prod-diff
172×times-frac
146×add-cube-cbrt
92×associate-+r+
58×difference-of-squares
44×distribute-lft-out
30×fma-neg distribute-lft-out--
14×associate-/r/
11×add-exp-log add-cbrt-cube add-log-exp
8×flip3-- flip-- div-inv
6×pow1
4×expm1-log1p-u log1p-expm1-u
3×tan-quot fma-def associate-*r* associate-*l* associate-/r*
2×cbrt-undiv sub-neg diff-log div-exp associate-*l/ prod-exp sum-log cbrt-unprod
1×+-commutative associate-+r- frac-2neg flip3-+ pow-prod-down clear-num *-commutative frac-sub flip-+ associate-/l/ associate-/l* unswap-sqr
Counts
4 → 295
Calls
4 calls:
165.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
109.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
5.0ms
(/ (* (tan y) (sin z)) (cos z))
5.0ms
(* (tan y) (sin z))

series997.0ms

Counts
4 → 12
Calls
4 calls:
385.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
425.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
108.0ms
(/ (* (tan y) (sin z)) (cos z))
79.0ms
(* (tan y) (sin z))

simplify111.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
08047012
125805836
250015650

prune978.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (tan a) 3)
0.4b
(* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))))
0.6b
(pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3)
1.3b
(/ (- (pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3) (pow (tan a) 3)) (fma (tan a) (+ (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))))))

rewrite715.0ms

Algorithm
rewrite-expression-head
Rules
408×*-un-lft-identity
400×add-sqr-sqrt
327×times-frac
152×difference-of-squares
120×add-cube-cbrt
105×unpow-prod-down cube-prod
60×distribute-lft-out--
56×distribute-lft-out
54×swap-sqr
42×sqr-pow
33×associate-/l*
30×associate-*r* associate-*l*
22×add-exp-log add-cbrt-cube
13×pow1
12×associate-/r/
7×flip3-- flip-- div-inv
6×cbrt-undiv pow-unpow div-exp
4×difference-cubes cube-div expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×pow-exp associate-/r* associate-/l/ rem-cube-cbrt
2×tan-quot cube-mult pow-to-exp pow-pow unpow3
1×pow2 frac-times frac-2neg pow-plus div-sub associate-*r/ pow-prod-down associate-*l/ clear-num pow-sqr *-commutative pow-prod-up frac-sub
Counts
4 → 405
Calls
4 calls:
2.0ms
(pow (tan a) 3)
84.0ms
(* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))))
20.0ms
(pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3)
576.0ms
(/ (- (pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3) (pow (tan a) 3)) (fma (tan a) (+ (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))))))

series3.4s

Counts
4 → 12
Calls
4 calls:
54.0ms
(pow (tan a) 3)
269.0ms
(* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))))
315.0ms
(pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3)
2.7s
(/ (- (pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3) (pow (tan a) 3)) (fma (tan a) (+ (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))))))

simplify188.0ms

Algorithm
egg-herbie
Counts
417 → 417
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0168219253
1500218408

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes391.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03645
13645

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.1s3945×body1280valid
923.0ms2010×body640valid
372.0ms8000×pre80true
207.0ms664×body320valid
108.0ms1092×body80valid
60.0ms289×body160valid