Details

sample392.0ms

Algorithm

intervals

Results

223.0ms	97×	body	1280	valid
63.0ms	59×	body	640	valid
61.0ms	21×	body	2560	valid
17.0ms	24×	body	320	valid
9.0ms	42×	body	80	valid
5.0ms	13×	body	160	valid

simplify16.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize15.0ms

Local error

Found 2 expressions with local error:

2.7b	(tan (+ x eps))
1.5b	(- (tan (+ x eps)) (tan x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `tan-quot` `add-log-exp`
2×	`pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 27

Calls

2 calls:

Slowest

13.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series170.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

104.0ms	(- (tan (+ x eps)) (tan x))
65.0ms	(tan (+ x eps))

simplify531.0ms

Counts: 40 → 33

prune287.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.7b

localize32.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b	(* (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))

rewrite134.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`insert-posit16` `associate-/l*`
3×	`associate-/r` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `flip3--` `frac-add` `associate-/r/` `flip-+` `flip--` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

Slowest

78.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
25.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
23.0ms	(* (tan x) (tan eps))
7.0ms	(+ (tan x) (tan eps))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

517.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
308.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
149.0ms	(* (tan x) (tan eps))
133.0ms	(+ (tan x) (tan eps))

simplify465.0ms

Counts: 123 → 102

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.6b

localize44.0ms

Local error

Found 4 expressions with local error:

6.7b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (+ (tan x) (tan eps)) (cos x))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`flip3--` `insert-posit16` `flip--`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `diff-log` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

Slowest

42.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
30.0ms	(* (+ (tan x) (tan eps)) (cos x))
26.0ms	(* (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))

series722.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

281.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
165.0ms	(* (+ (tan x) (tan eps)) (cos x))
141.0ms	(* (tan x) (tan eps))
134.0ms	(* (tan x) (tan eps))

simplify835.0ms

Counts: 108 → 98

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize70.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin x) (sin x))
0.2b	(* (tan x) (tan eps))
0.2b	(* (/ (cos x) (cos eps)) (sin eps))
0.2b	(/ (* (sin x) (sin x)) (* (cos eps) (cos x)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`add-cbrt-cube` `add-exp-log`
19×	`associate-l`
18×	`*-un-lft-identity` `add-cube-cbrt`
15×	`pow1`
11×	`times-frac`
9×	`associate-r`
8×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `div-exp`
4×	`tan-quot` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`swap-sqr` `pow-prod-down` `*-commutative`
2×	`associate-*l/` `sqr-sin` `div-inv` `sin-mult`
1×	`pow2` `frac-times` `clear-num` `associate-/r` `frac-2neg` `pow-plus` `div-sub` `associate-r/` `associate-/r/` `pow-sqr` `cos-mult` `pow-prod-up` `associate-/l*` `associate-/l/`

Counts

4 → 108

Calls

4 calls:

Slowest

28.0ms	(* (tan x) (tan eps))
25.0ms	(* (/ (cos x) (cos eps)) (sin eps))
16.0ms	(/ (* (sin x) (sin x)) (* (cos eps) (cos x)))
15.0ms	(* (sin x) (sin x))

series374.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

158.0ms	(* (tan x) (tan eps))
106.0ms	(/ (* (sin x) (sin x)) (* (cos eps) (cos x)))
82.0ms	(* (/ (cos x) (cos eps)) (sin eps))
26.0ms	(* (sin x) (sin x))

simplify649.0ms

Counts: 127 → 120

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes227.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch8.0ms

end0.0ms

sample14.2s

Algorithm

intervals

Results

7.3s	3336×	body	1280	valid
3.4s	1860×	body	640	valid
2.1s	622×	body	2560	valid
672.0ms	782×	body	320	valid
309.0ms	1070×	body	80	valid
207.0ms	330×	body	160	valid