Details

sample168.0ms

Algorithm

intervals

Results

84.0ms	105×	body	1280	valid
32.0ms	18×	body	2560	valid
28.0ms	62×	body	640	valid
6.0ms	17×	body	320	valid
5.0ms	40×	body	80	valid
3.0ms	14×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize9.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
4.4b	(tan (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

8.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series144.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(- (tan (+ x eps)) (tan x))
56.0ms	(tan (+ x eps))

simplify82.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune96.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
44.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series733.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(+ (tan x) (tan eps))
89.0ms	(* (tan x) (tan eps))
346.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	995

prune305.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
0.2b	(* (sin x) (tan eps))
3.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
5×	`tan-quot`
4×	`times-frac`
3×	`associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `clear-num` `sum-log` `-commutative` `frac-sub` `flip--` `flip-+` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

3.0ms	(+ (tan x) (tan eps))
5.0ms	(/ (* (sin x) (tan eps)) (cos x))
4.0ms	(* (sin x) (tan eps))
85.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series643.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (tan x) (tan eps))
102.0ms	(/ (* (sin x) (tan eps)) (cos x))
79.0ms	(* (sin x) (tan eps))
368.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	389	785
1	1406	711
2	5001	699

prune303.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
3.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
26.4b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`tan-quot`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`cube-div` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-r` `associate-l` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `times-frac` `pow1/3` `diff-log` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
4.0ms	(pow (* (tan x) (tan eps)) 3)
107.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
3.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series669.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (tan x) (tan eps))
128.0ms	(pow (* (tan x) (tan eps)) 3)
356.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
94.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify54.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	384	791
1	1733	746
2	5002	745

prune280.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.4b

regimes161.0ms

Accuracy

87.8% (0.9b remaining)

Error of 15.5b against oracle of 14.5b and baseline of 22.2b

bsearch188.0ms

Steps

Iters	Range		Point
9	2.450734406407808e-49	1.8905107981278726e-44	1.8727168353926166e-44
8	-2.2913029590799255e-75	-9.949878853385243e-80	-1.9052490692525806e-75

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	49
1	55	49

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.7s	3341×	body	1280	valid
1.1s	636×	body	2560	valid
920.0ms	1845×	body	640	valid
238.0ms	729×	body	320	valid
143.0ms	1101×	body	80	valid
95.0ms	348×	body	160	valid